In many letters about piezoelectric materials like PZT, PLZT, author shows P-E curve which is illustrated by hysteresis loop shape or dielectric constant
Does anyone know about relationship between polarization in P-E hysteresis curve(or dielectric constant or coercive field... etc) and piezoelectric constant (d33)?
If piezomaterials have large polarization value, they have large d33? or they haven't any relationship??
If polarization was measured properly it can give an idea about the piezoelectric response. However the relation is not straightforward because:
- polarization measurements are affected by leakage currents;
- piezoelectric response is affected by the rigidity of structure, clamping, defects, microstructure, geometry of force head that was used for measurements, etc.
There is a couple of good reviews on ferroelectric/piezoelectric properties. My favourite is this one: Damjanovic, D. (1998). Ferroelectric, dielectric and piezoelectric properties of ferroelectric thin films and ceramics. Reports on Progress in Physics, 61(9), 1267–1324. http://doi.org/10.1088/0034-4885/61/9/002
As we know the electric displacement is given by:
D = E + 4πP
where E is the electric field and, P is the total polarization
Now according to the below relation we can find and understand the relation between d33 and the total polarization:
d33= Int (Eps33*E3*dA)/Int(sigma*dA);
where Eps33 is the dielectric constant,
E3 is the electric field in the z direction
sigma is the normal stress
For more information you can download:
http://depts.washington.edu/solgel/documents/pub_docs/journal_docs/2013/VIB-11-1084_Published.pdf
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